2014/06/04 by Karen Yagdjian, Yagdjian, Karen · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Nonlinear Waves and Solitons #Numerical methods for differential equations #math-ph #math.AP #math.MP #msc:35C15 #msc:35Q75
paper · pdf · doi:10.48550/arxiv.1406.1254
arxiv created 2014/09/01 · arxiv updated 2014/09/02
In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave equation, and then it was used to investigate several well-known equations such as Tricomi-type equation, the Klein-Gordon equation in the de~Sitter and Einstein-de~Sitter spacetimes. A generalization given in this paper allows us to consider also the Klein-Gordon equations with coefficients depending on the spatial variables.